Understanding the electrochemical reaction mechanisms and kinetics in batteries is the key challenge for developing breakthroughs with new or existing electrode materials. X-rays and neutrons are excellent probes for studying atomic structure changes and phase evolution in battery materials during charge and discharge. Synchrotron X-ray powder diffraction (SXPD), with its high angular resolution and beam intensity, allows fast scattering and diffraction data collection to record crystalline structure changes that occur on short time-scales. Neutron powder diffraction (NPD) provides complementary information that is sensitive to different structural details during charge/discharge. More recently X-ray absorption spectroscopy (XAS) has been used to identify the oxidation states of transition metal ions present in new cathode compositions at different stages of battery cycling. Using in-house designed battery cells, electrodes or other cell components can be subjected to conditions designed to mimic their real operating conditions. It is preferable to investigate battery materials in operation to identify any critical intermediate stages during charge/discharge rather than using ex situ methods to analyse dismantled batteries. Examples and combinations of SXPD, XAS, and NPD measurements, which have been used to investigate lithium ion batteries and sodium ion batteries, are described and reviewed in this contribution.